Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analysed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean-velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from Taylor’s hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The free-stream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the free-stream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( ${>}300\delta _i$ , with $\delta _i$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $Re_\tau \approx 1200$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region.

Direct numerical simulations are used to examine the pressure fluctuations generated by fully developed turbulence in a Mach 2.5 turbulent boundary layer, with an emphasis on the acoustic fluctuations radiated into the free stream. Single- and multi-point statistics of computed surface pressure fluctuations show good agreement with measurements and numerical simulations at similar flow conditions. Consistent with spark shadowgraphs obtained in free flight, the quasi-homogeneous acoustic near field in the free-stream region consists of randomly spaced wavepackets with a finite spatial coherence. The free-stream pressure fluctuations exhibit important differences from the surface pressure fluctuations in amplitude, frequency content and convection speeds. Such information can be applied towards improved modelling of boundary layer receptivity in conventional supersonic facilities and, hence, enable a better utilization of transition data acquired in such wind tunnels. The predicted acoustic characteristics are compared with the limited available measurements. Finally, the numerical database is used to understand the acoustic source mechanisms, with the finding that the supersonically convecting eddies that can directly radiate to the free stream are confined to the buffer zone within the boundary layer.

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.